The well-deserved popularity of Rhodes as a holiday destination means that airlines are queuing up to take you there; so you have the opportunity to shop around and find some really good deals. British Airways is a great example; offering return flights form Gatwick for under £150. Prices vary wildly depending on your departure airport and exactly when you plan to travel.
If you are looking for a cheap flight to Rhodes ; Excel Airways is a tried-and-tested starting point. You need to be flexible, as Excel only flies on Wednesdays during the summer months, but you can bag seats for as little as £100 return. Excel is a popular choice for anyone living outside the capital as they operate flights from Bristol and Birmingham.
If you're happy to head to London, see what Monarch Airlines has to offer. They only fly from Gatwick, and regular published fares might not be as cheap as the airlines already mentioned, but Monarch is well-known for offering promotional discounts. If you're a dedicated cost-saver, sign up to their electronic mailing list to make sure you won't ever miss a deal. Another option is Olympic, who flies from Heathrow. Again prices aren't always the lowest, but you can pick up some serious bargains.
Rhodes Airport has undergone considerable modernization in recent years, although it still manages to have a slightly unkempt feel about it. The airport is situated eight miles from the city centre and you have a number of ways of making the short trip. Taxis queue up outside the airport and shouldn't charge more than £10, although you may be stung for extra baggage. At the time of writing, there wasn't an airport bus as such, but you can catch frequent city buses from the main road a few minutes' walk away. If you want to hire a car you'll find all the usual players represented in the airport arrivals hall; plus a couple of local outfits including Argus.